A simplified multi-objective analysis of optimum profile modifications in spur and helical gears

• A unique equation for optimum profile relief with respect to transmission error
• Analytical formulations for contact, root stresses and friction losses
• The analytical results compare well with more time-consuming numerical simulations.
• Multi-objective performance diagrams for profile modifications are presented.
• Guidelines are given for the choice of optimum profile modifications.

A simplified analysis is presented in order to evaluate the influence of the profile modifications minimising transmission error time-variations on some other key design criteria such as mesh forces, stresses and tooth friction losses. A unique equation for the set of profile modification rendering transmission error nearly constant is presented and a number of original stress and loss factor closed-form formulae are derived whose results compare very well with those obtained by numerical simulations. Some general results are then deduced about the evolutions of the design criteria with regard to optimum relief parameters which are believed to be useful at the early stage of profile modification design.